(CBS News) The NAACP says more than 400,000 people have signed its online petition urging the Justice Department to pursue criminal civil rights charges against George Zimmerman.
CBS News correspondent Michelle Miller spoke with Ben Jealous, president of the NAACP, at the organization's convention in Orlando.
"The justice system still has more to do it's not over yet," Jealous said.
He said Trayvon Martin's supporters have a clear idea of how the Justice Department can get involved.
"They would step in and file federal civil rights charges probably based on the Matthew Shepard and James Byrd, Jr. Hate Crimes Prevention Act, which says that in effect a hate crime is a hate crime wherever it happens," Jealous said.
Jealous said he and others like him respect the outcome of the trial in Florida, but they would still like to see more happen.
"We put our faith in our justice system," Jealous said. "We ultimately accept this verdict, but just as we accept this verdict, the country should accept that we have civil rights laws for a reason. There is more that can be done and should be done."
Full coverage of the George Zimmerman trial & Trayvon Martin case
In a statement, the Department of Justice said it is reviewing evidence in the state's case against Zimmerman to see if there is enough to support criminal civil rights charges.
There should be no concerns about whether this would amount to "double jeopardy" because Zimmerman was exonerated in a Florida court on Saturday, said CBS News legal analyst Jack Ford on "CBS This Morning." (Watch the full interview with Ford at left.)
"If he was tried again it wouldn't be for murder and manslaughter," Ford said. "There's certain situations where different sets of facts and circumstances give rise to different federal and state charges."
However, the attorneys in the Justice Department aren't always eager to pursue their own cases, Ford said.
"The Justice Department is always very cautious when there's been a state level trial," Ford said. "There has to be very high standard. It's not enough just for people to disagree with the verdict. The Justice Department will jump in if there was a failure to investigate, or a failure to prosecute."
In the case of George Zimmerman, it is unlikely but not impossible that federal prosecutors will get involved.
"Statistically it's not probable it will happen, but we've seen in the past, for instance the Rodney King case, it's certainly possible that the Justice Department can say, 'We're going to process the civil rights violation of attacking Trayvon Martin because he was black,'" Ford said.
In order for a federal case to go forward, the prosecution would have to show racial animus on the part of Zimmerman.
"They would have to show George Zimmerman violated Trayvon Martin's civil rights, the right to be safe and not attacked because of his race," Ford said.
A much more likely second round of litigation for Zimmerman would be a civil trial between the families. A good comparison is the O.J. Simpson case, where Simpson was exonerated in the criminal trial but sued in a civil trial by the family of the deceased, Ford said.
"The standard of proof in a civil trial is much, much lower," Ford said. "In a civil trial, they can compel George Zimmerman to testify."
Ford said Zimmerman criminal trial was hard for the prosecution to prove from the outset.
"The reality is with trials and verdicts there's always disagreements," Ford said. "But here there shouldn't be a great surprise."